A cluster state can be loosely defined as an entangled set of qubits arranged in a lattice. Breigel and Raussendorf strictly define a cluster state as “Let each lattice sight be specified by a d-tuple of (positive or negative) integers aεZd. Each sight has 2d neighboring sights. If occupied they interact with the qubit a”. This implies a cluster state has interaction between all nearest neighbor qubits. In two dimensions (d=2) this can result in a square grid of qubits, of arbitrary size and shape with each qubit connected to up to 4 of its nearest neighbors. All of the internal qubits will have 4 interactions while the edge qubits will have 1, 2, or 3 interactions. Such a two dimensional nearest neighbor (or square) cluster state has been shown to be universal for computation presuming the cluster state is “large enough”. It is however possible to create custom cluster states designed to implement a single type of algorithm with less qubits.
Traditional generation of a cluster state consists of an optical table several meters on a side. On this table is a high power laser system such as a pulsed Ti:Sapphire laser. The pump beam is incident on a nonlinear material such as BBO, BiBO or PPKTP etc. The photons from the pump then have a small change to undergo Spontaneous nonlinear Parametric Down Conversion (SPDC) to create an entangle pair of photons, called signal and idler photons. Alternative means of photon generation are equally valid such as Four Wave Mixing (FWM). To create larger clusters the pump passes through multiple nonlinear materials (a cascade) or is reflected back onto it (a multi-pass pass). These methods can create multiple independent pair of qubits. To create one large cluster state the pairs are sent through (i.e. acted on by) a maximally entangling gate. Normally the Controlled Z Gate or “CZ” gate is used. The simplest and most efficient means of implementing the CZ gate requires 3 bulk optical asymmetric beamspliters in a specific alignment. Once all the entangling operations are successfully complete the cluster state is fully constructed and an algorithm can be implemented as a sequence of measurements each on a predetermined qubit.
Generating cluster states beyond four qubits and one CZ gate represent significant experimental difficulties. The SPDC action is relatively inefficient, especially for generating large numbers of photon pairs. The probability of generating n+1 pairs compared to n pairs is approximately 1/1000. This number varies with setup and nonlinear material but is a useful rule of thumb. Thus it rapidly becomes unlikely that a sufficient number of photons are generated in any one time window. Also the CZ gate itself is probabilistic, with a success rate of 1/9. Thus each entangling operation decreases the rate of successful cluster state construction by nearly an order of magnitude. To generate statistics for large cluster state operations, experimentalists are routinely required to wait minutes even hours between successful cluster state generation events.
A significant improvement on cluster state generation is possible with on demand photon sources. Such a source emits a single photon or pair of photons at a specified time, eliminating the need for probabilistic photon generation. No such device currently exists. As an approximation to an on demand source, the “photon gun” was recently proposed by Mower Englund (WO2013009946 A1). This device remains probabilistic but has a relatively high probability of producing a single photon at a predetermined time and is in fact intended to be periodic. In other words it will with relatively high probability emit a single photon after time T. The photon gun creates pairs of photons via probabilistic means from time 0 to T−1 and then detects (and thus destroys) the presence of one of those photons to herald the presence of the remaining photon. This heralded photon is then delayed in a variable circuit until time T. The device is nearly periodic because the probability of at least one pair being generated before time T−1 is close to 1. Thus the photon gun sacrifices repetition rate in order to maximize the photon production probability.